In some CPU heavy games, the 6600 will hold back the 2070. In games that are not CPU heavy, then it wont.
While I like the 2600 and it is a good CPU, in your case I would not go for it. I would look for a used 6700/7700. If you have a "z" board, then you can go for a "k" CPU, if not then I would go with the non "k" chip.
They will have enough threads for CPU heavy games and have better single threaded performance than a 2600. You will also not need a new mobo as they will drop into your current board. If you go for a 7th gen CPU, you will need a bios update, but that is pretty straight forward.